The Role of Purkinje-Myocardial Coupling during Ventricular : A Modeling Study

Elham Behradfar1*, Anders Nygren1, Edward J. Vigmond1,2 1 Department of Electrical and Computer Engineering, University of Calgary, Calgary, Alberta, Canada, 2 Institut LIRYC and Laboratoire IMB, Universite Bordeaux 1, Bordeaux, France

Abstract The Purkinje system is the fast conduction network of the heart which couples to the myocardium at discrete sites called Purkinje-Myocyte Junctions (PMJs). However, the distribution and number of PMJs remains elusive, as does whether a particular PMJ is functional. We hypothesized that the Purkinje system plays a role during reentry and that the number of functional PMJs affect reentry dynamics. We used a computer finite element model of rabbit ventricles in which we varied the number of PMJs. Sustained, complex reentry was induced by applying an electric shock and the role of the Purkinje system in maintaining the arrhythmia was assessed by analyzing phase singularities, frequency of activation, and bidirectional propagation at PMJs. For larger junctional resistances, increasing PMJ density increased the mean firing rate in the Purkinje system, the percentage of successful retrograde conduction at PMJs, and the incidence of wave break on the epicardium. However, the mean firing of the ventricles was not affected. Furthermore, increasing PMJ density above 13/cm2 did not alter reentry dynamics. For lower junctional resistances, the trend was not as clear. We conclude that Purkinje system topology affects reentry dynamics and conditions which alter PMJ density can alter reentry dynamics.

Citation: Behradfar E, Nygren A, Vigmond EJ (2014) The Role of Purkinje-Myocardial Coupling during Ventricular Arrhythmia: A Modeling Study. PLoS ONE 9(2): e88000. doi:10.1371/journal.pone.0088000 Editor: Alexander V. Panfilov, Gent University, Belgium Received November 19, 2013; Accepted January 3, 2014; Published February 7, 2014 Copyright: ß 2014 Behradfar et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was in part supported by a grant from the National Institutes of Health, grant number R01HL101196. This work was also partly supported through the Investment of the Future grant, ANR-10-IAHU-04, from the government of France through the Agence National de la Recherche. The funders hadno role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: [email protected]

Introduction PMJ density may change due to increases in heart size, as during dilated (DCM) for example, or alterations The Purkinje System is the fast conduction system of the heart, in Purkinje system structure, for example, due to aging [5]. responsible for ensuring coordinated contraction of the ventricles. has also been shown to alter the number of functional Despite its importance, many important small details remain PMJs [6] as have changes in cellular coupling [4]. PMJ density was unknown, and these details affect electrical wave propagation at shown to have an effect in a model of biventricular pacing [7] but the whole organ level. Recording Purkinje system activity using its effect on reentry dynamics are not known. More PMJs can lead multielectrode catheters has provided some insights into Purkinje to more retrograde conduction and allow more escape paths for system involvement in ventricular (VF): Bidirectional but can also decrease tissue heterogeneity. Thus, its propagation between Purkinje system and myocardium has been actions are both pro- and antiarrhythmic [8]. From a modeling observed during VF in canine heart [1]; cryoablation of canine perspective, given studies by our group using simplified Purkinje changed the activation pattern of VF [2]; and system representations[9–11], it is important to know if results are chemical ablation of Purkinje system led to faster termination of relevant given the true complicated Purkinje system structure. VF and lower activation rate in dogs [3]. However, the spatial This study hypothesized that PMJ density has an effect on resolution obtained by this technique is not sufficient for direct reentry dynamics, and sought to determine the minimum density detection of electrical activity of the Purkinje system since its to incorporate into models. This was done by initiating fibrillation extremely fine structure prevents recording its activity over a large in a biventricular computer model and quantifying reentry area. Furthermore, even methods which have successfully characteristics as a function of PMJ density. We also performed reconstructed the topology of the endocardial network have been a sensitivity analysis of the parameters used to control activity unable to map the insertion of the Purkinje system into across the PMJ structure. myocardium where it forms Purkinje-Myocyte Junctions (PMJs), which are responsible for activating the ventricular muscle. Methods Finally, even if the PMJs are imaged, be it by histology or otherwise, their functional role still requires electrophysiological Purkinje Network Modeling evaluation since evidence points to a large number of nonfunc- To develop an anatomically detailed model of Purkinje system, tional junctions [4]. To date, the number and distribution of we used a fractal method [12] to extend the Purkinje network that functioning PMJs is unknown and no technique currently exists to had been manually constructed by our lab [13], shown in Fig. 1A directly measure it. in red. To grow new branches of Purkinje system on the

PLOS ONE | www.plosone.org 1 February 2014 | Volume 9 | Issue 2 | e88000 Modeling Purkinje-Myocardial Coupling endocardial surface, endpoints of the manually constructed grade delays. Anterograde delay times in the range of 4–14 msec network were used as starting points. The growth process was and retrograde delay times between 2–4 msec were considered based on extended L-system and a generating rule suggested by physiological [16,17]. Combinations of RPMJ and NPMJ values Ijiri et al [12]. The parallel rewriting system replaces each part of resulting in realistic transmission characteristics were in the ranges the current structure by applying the rule sequentially and 10–25 MV for RPMJ, and 10–30 for NPMJ: generates a uniform distribution of branches on the endocardial surface. Endocardial surfaces were extracted from an FEM model VF Induction in Ventricle Model of the rabbit ventricles and the outcome was two triangularly Computer simulations were performed on an image based meshed surfaces. Each new generated point was projected onto the computer model of rabbit ventricles complete with Purkinje system closest triangle of the endocardial surface at each iteration, thereby as used extensively by our group[8–11,13,18]. Cardiac electrical ensuring the Purkinje system exactly lay on the endocardium. activity was described by the bidomain equations [19] which relate Adjusting the parameters of L-system was based on comparisons the intracellular to the extracellular potential through transmem- with photographs of actual rabbit Purkinje system [14] and brane current density. The system of equations was solved by the activation patterns in rabbit ventricles. The branch length was set finite element method using the Cardiac Arrhythmias Research to 2 mm and each branch consisted of five line segments to obtain Package (CARP) [20]. Ion dynamics for the myocardium were a more realistic branch curvature. Fig. 1A illustrates extended described by the rabbit ventricular action potential (AP) model branches connected to 53 endpoints of the manually constructed developed by Mahajan et al. [21], while the Purkinje cell of network. Aslanidi et al. [22] was used for the Purkinje system. The next step of constructing the Purkinje system model was to Reentry was initiated through an S1–S2 protocol: for S1, two add the endpoints, which contact with ventricular myocytes and His paces were delivered 500 ms apart. S2 was an extracellular activate them through PMJs. In light of the dearth of data on cross shock delivered by applying a uniform electric field via two PMJs, endpoints were uniformly distributed on extended branches planar electrodes at bath boundaries oriented along the plane of of Purkinje system by setting a minimum distance between them the ventricular septum. S2 followed S1 after a variable coupling and then inserting them into the myocardium up to 20% of wall interval (CI). The strength of the shock and the CI between S1 and thickness. To create various PMJ densities, seven different values S2 were varied to find combinations that induced sustained for the minimum distance between Purkinje system endpoints reentry, that which lasted for at least 3 s. were set. In the end, Purkinje system models with 74, 105, 166, To better model responses to electric shocks, ionic models were 244, 325, 451 and 516 PMJs were generated. Fig. 1B and C shows modified to include an electroporation channel [23] and an the new Purkinje system models with different PMJ density and outward current activated during shock-induced depolarization the activation sequence after His stimulation. The total activation [24]. To facilitate VF induction, ICaL (L-type Ca current) recovery time of Purkinje system was about 25 ms. from inactivation kinetics was increased for the intermediate range Mathematical details of the PMJ structure and its coupling to of diastolic interval (DI) values (10–50 ms). myocardium are found in [13]. In brief, at each PMJ, a Purkinje element was coupled to the NPMJ closest myocardial points by a Data Analysis fixed resistance RPMJ. The current load on each terminal Purkinje For assessing the role of the Purkinje system and Purkinje- cell was calculated by summing the individual currents flowing myocardium coupling during arrhythmia, reentry dynamics were into each junctional myocyte and scaling the total by a loading evaluated using three measures: 1) Mean firing rate (MFR) was factor KPMJ to account for myocardial loading effects from quantified for every node of the tissue model, by inspecting surrounding tissue. This implementation was designed to attain membrane voltage (vm) and counting activations by threshold discontinuous and asymmetric propagation across the PMJ [15]. crossing at 220 mV with a 50 ms blanking interval. MFR was The sensitivity of transmission delay to changes of PMJ model calculated by dividing the number of activations by the duration of parameters was evaluated and parameters were sought to match the associated counting interval which was 3 s here. experimental measurement. Propagation delay at PMJs was 2) A useful measure for evaluating spatial organization of VF is defined as the difference between activation time of the terminal the number of phase singularities that form during VF. An Purkinje node and the average activation time of coupled algorithm to detect phase singularities was used which relied on myocytes. We found a range of values of junctional parameters the intersection of two isosurfaces which were computed at a (RPMJ,NPMJ) which resulted in realistic anterograde and retro- certain temporal interval [25]. This reduces to finding points or

Figure 1. 3D model of Purkinje network. A) new model of Purkinje network consists of manually constructed branches (red) and extended branches (blue) B) Purkinje system model with lowest PMJ density (74 PMJs) and its activation map for His bundle stimulation C) Purkinje system model with highest PMJ density (516 PMJs) and its isochronal activation map. doi:10.1371/journal.pone.0088000.g001

PLOS ONE | www.plosone.org 2 February 2014 | Volume 9 | Issue 2 | e88000 Modeling Purkinje-Myocardial Coupling lines along which the temporal derivative is zero. Filament analysis from the anterior and posterior perspectives. Activation in was carried out with the isosurface threshold set to 240 mV and ventricles started from the medial or apical part of the right the interval between slices set to 8 ms. We then calculated the ventricular free wall and propagated toward the base of heart. In WaveBreak Incidence (WBI) [26] by counting the phase singular- the left ventricle, the action potential broke through towards the ities on the epicardium and endocardium surfaces separately, and septum and apex. Similarity, the activation patterns for the three normalizing by the surface area and the average number of PMJ densities depicted in Fig. 3 suggest that the number of excitation cycles estimated as the product of MFR and reentry uniformly distributed PMJs does not considerably affect the duration. An increase in WBI indicates a more complex sequence of ventricular activation. For the model with 74 PMJs, arrhythmia since there are more phase singularities. 3) We also the ventricles were entirely activated after 66 ms, and with 516 counted the number of successful and failed anterograde and PMJs, this time reduced to 58 ms. retrograde propagations during reentry in the whole model, which Right and left basal regions excited at the end of this interval. directly shows the contribution of the Purkinje system to the Epicardial activation sequences were compared to those obtained reentry circuit. A conduction at the junction was considered from ventricular epicardial unipolar electrograms and optical successful when the terminal Purkinje node and more than 50% of mapping of a rabbit heart during sinus rhythm [27,28]. The early coupled myocytes activated within a reasonable time interval for epicardial breakthrough sites reported in theses experimental anterograde and retrograde propagations, otherwise conduction at studies are right ventricle freewall and left ventricle apex. the PMJ was considered to have failed. The acceptable time Activation spread generally from apex to base and finally to the interval was selected as 8 ms for retrograde propagation and left ventricle base. Although the total activation time measured 16 ms for the reverse direction. When vm started below 260 mV experimentally is shorter than what we found, the predicted and depolarized above 220 mV, it was counted as an AP. Fig. 2 activation sequence using our model was similar to the experi- illustrates examples of successful and failed retrograde and mentally measured activation sequence. anterograde conductions for a PMJ during 3 s VF. PMJ parameters were chosen such that starting from the resting state, Effect of PMJ Density propagation was always successful. Failure occurred due to The earliest propagated post-shock activation which initiated dynamical properties of the junction, most commonly that the reentry originated from the Purkinje system in all simulations. To the post junctional tissue was refractory, rapid activation possibly reducing available sodium current, or a combination of the two. clarify the role of the Purkinje system and especially Purkinje- myocardium coupling during maintenance of reentry, we studied reentry patterns 2 s after initiation of reentry. At this stage, the Results transient have died down and a more stable reentry has been Sinus Activation established. The extended Purkinje system was superimposed on the Fig. 4A shows a snapshot of VF generated by sustained reentry endocardium of rabbit ventricles model and sinus rhythm was along with phase singularities detected on the epicardium. The simulated by stimulating the His bundle. The resultant activation complicated patterns of VF were driven by simultaneous sources of sequence for Purkinje systems with different PMJ densities were functional reentry. The Purkinje system favors reentry by compared. The time of first breakthrough on epicardium varied providing pathways through retrograde and anterograde conduc- from 18 to 26 ms which was inversely proportional to PMJ tion at PMJs However Purkinje system involvement in reentry may density. Fig. 3 illustrates the epicardial isochronal activation maps stop propagation of excitation in certain direction or fractionate

Figure 2. Instances of conduction success and failure at one PMJ. A) successful retrograde propagation, B) failed retrograde propagation C) failed anterograde propagation D) successful anterograde propagation. doi:10.1371/journal.pone.0088000.g002

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Figure 3. Activation maps for different PMJ densities. Excitation of the ventricular myocardium by the Purkinje system during sinus rhythm for Purkinje system models with three different numbers of PMJ as indicated on the left. Activation time since His bundle stimulation is scaled between earliest and last epicardial activation over all simulations. doi:10.1371/journal.pone.0088000.g003 reentrant wavefronts due to refractory regions surrounding PMJs, As can be seen in Fig. 2, the activation pattern at a particular which consequently increased the complexity of excitation PMJ had little consistency over time and bidirectional conduction dynamics. These antagonistic effects have been described previ- and block occurred, indicative of functional reentry. Filaments in ously [8,18]. the ventricles are displayed in Fig. 4B which shows most of the wavebreaks were associated with Purkinje system activity. Most of

Figure 4. Purkinje system contribution during reentry. A) Rotors on the epicardium surface along with phase singularities indicated by red asterisks. B) Filaments in ventricles colocalized with Purkinje system endpoints. I-shaped filaments which terminate close to Purkinje system endpoints are shown in green, and O-shaped filaments which formed close to Purkinje system endpoints are indicated in orange. Surface phase singularities are as in A. doi:10.1371/journal.pone.0088000.g004

PLOS ONE | www.plosone.org 4 February 2014 | Volume 9 | Issue 2 | e88000 Modeling Purkinje-Myocardial Coupling the transmural I-shaped filaments were anchored to Purkinje system is higher for larger number of PMJs (Fig. 5B). Average system endpoints and O-shaped filaments formed close to the MFR in the ventricular mass changed in the narrow range of 7.8– Purkinje system endpoints. 8.2 Hz and did not show a sensitivity to junctional parameters or Fig. 5 illustrates how changes in PMJ density affected reentry. PMJ density Although there was a direct relation between the The number of failed and successful propagations increased number of successful anterograde propagations and the average monotonically as the density of PMJs in the model increases, either MFR in ventricles, changes in ventricular MFR were not for retrograde or anterograde transition. The portion of successful considerable. In the cases that reentry was not sustained and propagations for different PMJ densities are shown in Fig. 5. In lasted for less than 3 s, the number of successful anterograde models with higher numbers of PMJs, the contribution of the propagations, the average MFR in ventricles, and the WBI were Purkinje system increased. More successful bidirectional propaga- all lower compared to sustained reentry which demonstrates the tion at PMJs showed a more significant role of the Purkinje system interplay among these three parameters. in establishing the reentrant pathway,and a better synchronization An increase in successful anterograde propagation correspond- of activity. Generally, anterograde propagation was more success- ed to a higher WBI on the epicardium, while the number of ful than retrograde since the myocardium had a shorter APD and successful retrograde transmissions closely followed the endocar- higher MFR, lessening chances of myocardial tissue being dial WBI (see Fig. 5C). Successful anterograde propagation could recovered when activity tried to emerge from the PMJ. initiate a new epicardial breakthrough, leading to the collision of The number of successful retrograde transmissions of APs to the the new wave with existing meandering wave fronts, causing a new Purkinje system is an indicator of the degree to which ventricular wavebreak. When anterograde propagation was unsuccessful, activity drives Purkinje system activity; thus the increase of MFR activation did not spread in the ventricles and refractoriness in the Purkinje system was linked to the number of retrograde around the Purkinje system endpoint was prolonged, potentially propagations. This can explain why the MFR in the Purkinje leading to more wave front fractionation, generating more

Figure 5. Changes in reentry dynamics as a function of PMJ density. A) Portion of successful junctional propagations as a function of PMJ density B) Average MFR in ventricles and Purkinje system as a function of PMJ density C) WBI on epicardium and endocardium as a function of PMJ density (RPMJ =20MV, NPMJ = 20). doi:10.1371/journal.pone.0088000.g005

PLOS ONE | www.plosone.org 5 February 2014 | Volume 9 | Issue 2 | e88000 Modeling Purkinje-Myocardial Coupling wavebreaks. A higher WBI on the endocardium signified more [28], or by immunoenzyme labeling of a marker protein [14,29]. wavefronts and, hence, more chance for a wavefront to find a As an alternative, like in this work, fractals have been used to build recovered PMJ to enter. This follows since the Purkinje system is a 3D anatomical models of the HisJPurkinje network through rapidly conducting cable network which implies that cells over a automatic or semiautomatic procedures [12,28–30]. Our Purkinje large region are in a similar phase. With more wavebreaks, the system model was designed in two steps: first, main fascicles and myocardium displays more phases over a smaller region and the branches were created manually based on schematics and pictures odds of finding the proper combination of Purkinje system and of the conduction system and excitation mappings of the heart myocardial phases for retrograde reentry are greater. [13]. Second, detailed structures and endpoints generated by rewriting rules automatically. Since endpoints were only added to Effect of Junctional Characteristics the extended branches of Purkinje system model and not to the We also conducted a set of simulations to study how junctional manually constructed branches, the ventricular activation se- characteristics altered the interaction between the Purkinje system quence with extended Purkinje system is similar to that with and ventricular tissue during fibrillation with three different PMJ manual Purkinje system model. Also as reported in experimental numbers: 105, 244 and 455. studies [14], the Purkinje system in the left ventricle is more During sinus rhythm, the average delay time between the developed than that in the right ventricle, probably a result of activation of a terminal Purkinje system cell and coupled myocytes function, and our extended model contains more branches in the was calculated and sensitivity of latency to resistance and size of left ventricle. There is limited knowledge about the number and the junction were investigated. We found that variations in distribution of PMJs in ventricular tissue but it is found that there junctional resistance were directly related to changes in forward are not any junctions in basal and top portion of septal regions of and reverse transmission delays at the PMJ. An increase in the size ventricles in different species [29]. We took these features into of the junctions (number of coupled myocytes) shortened account to construct a Purkinje system model which replicates anterograde and retrograde delays. Reduction of the transmission known characteristics of the junctions. delay for anterograde and retrograde propagation is the result of decreased electrical loading at the junction which increases the Effect of PMJ Density safety factor for propagation. Our rabbit model varied the number of PMJs from 104 to 516 2 We assessed the consequences of changes in resistance of PMJ Given an endocardial surface area of 16.57 cm , this corresponds 2 (RPMJ) on reentry dynamics. For a larger PMJ resistance, there to densities ranging from 4.46 to 31.14 PMJs/cm . Scaled to a were generally fewer retrograde propagations (Fig. 6A and B), and human heart, this would implicate 1000 to 5000 PMJs. With more the effect was greater for fewer junctions. Increasing the resistance PMJs, the activations sequence did not change considerably, but tended to increase the MFR for the denser Purkinje system the time to activate was reduced. Part of the reduced time could be networks, while WBI was decreased. a consequence of the Purkinje system extending farther toward the Effects of PMJ size, NPMJ, on reentry dynamics were base to accommodate more PMJs. investigated by calculating MFR, WBI and the number of PMJ density did not affect the mean myocyte firing frequency propagations at PMJ. For both forward and reverse propagation during VF which was constant at 8 Hz. However, the Purkinje at the PMJ, as the PMJ enlarges, the number of failed system MFR did increase, albeit slightly, with the number of PMJs, propagations decreased more than successful ones which means but only up to 325 junctions. This roughly corresponds to the that the transmission of action potentials at the PMJ was easier. trend in the percentage of successful propagations at the junction Fig. 7 demonstrates that for a larger PMJ size, there is a lower which generally increased with the number of PMJs. The limit of MFR in the Purkinje system. In spite of lower values of MFR in 325 also agrees well the the epicardial WBI dependence on PMJs. the Purkinje system, the number of successful anterograde Since Purkinje system APs are intrinsically longer than ventricular propagations does not decrease with an increase of junction size, ones, the upper limit of the Purkinje system MFR is lower than implying that the Purkinje system more successfully activates the that of the ventricles. However, if the activity is better myocardium after the increase in size of the junction and as a synchronized between the Purkinje system and ventricles, more result, the WBI is higher (Fig. 7B). successful junctional transmissions will occur and drive the Purkinje system MFR towards the maximum. Discussion Interestingly, the endocardial WBI slightly decreased with higher PMJ density. The behavior most closely followed the ratio We have implemented a fractal method for growing the of retrograde success. Successful retrograde propagation would Purkinje system to allow investigation of PMJ density on reentry mean that endocardial wavefronts would reenter the Purkinje dynamics, something which has not been previously explored. We system and not interact with a refractory PMJ, possibly otherwise varied coupling parameters over a wide range, but stayed within resulting in wave fractionation and an increase in WBI. Since the physiological bounds as determined by transmission delays. Our WBI was higher on the epicardium, the filaments could not all be simulations are the first to gauge the contribution of the Purkinje transmural I-filaments since this would imply an equal endo- and system to reentry during shock-induced VF. We are able to epi-cardial WBI. Instead some U-filaments with both termini on conclude that there is a greater effect with a higher PMJ density. the epicardium must have been present. Comparing a variety of quantitative metrics, the dynamics of sustained reentrant arrhythmias were found to vary marginally for Effect of Purkinje-myocardium Coupling different coupling strengths at PMJs. We have used a continuum model although at a fine scale this In spite of many efforts to extract Purkinje network from does not hold. The Purkinje system begins as a bundle of fibres imaging data, it has not been extensively modeled in detail, due to which do not bifurcate. Whether or not Purkinje fibres do its intricate structure and subendocardial penetration. Realistic bifurcate and, if so, at which point is not known. At the PMJ, we geometrical models of the free running specialized conduction have resorted to a phenomenological approach to incorporate system have been constructed. In these studies, Purkinje system asymmetric transmission. The PMJ radius corresponds to the structure has been extracted from segmentation of MRI images terminal ‘‘branching’’ of the Purkinje system and the size of the

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Figure 6. Effects of PMJ resistance on reentry. A) Ratio of successful retrograde propagations to failed and successful retrograde propagations as a function of PMJ resistance B) Sensitivity of average Mean Firing Rate in Purkinje system to the resistance of PMJ C) Sensitivity of WBI on epicardium to resistance of PMJ (NPMJ = 20). doi:10.1371/journal.pone.0088000.g006 region stimulated by concurrent Purkinje system activity. A greater the interactions of filaments with Purkinje system endpoints. radius means more myocardial cells are simultaneously activated Previous modeling studies also suggested the presence of phase and they may be thought of as a functional unit. singularities around the distal Purkinje system network [18]. The coupling resistance is another important parameter. The In the presented model of the PMJ, the increase of electrical range of values supporting propagation across the junction is loading through increasing junctional resistance RPMJ or reduc- actually quite limited since too large of a value does not allow tion of junctional size NPMJ, increases transmission delay across enough charge to pass quickly enough to charge the postjunctional the PMJ for both directions. Sensitivity of anterograde delay to membrane, and too low of a value leads to excessive electrotonic junctional parameters is more significant than that for retrograde loading which suppresses prejunctional action potentials. conduction. Also propagation delay varies considerably more for The Purkinje system involvement in VF strongly depends on changes of RPMJ rather than changes of NPMJ. Purkinje-myocardium coupling as it affects bidirectional propaga- The impact of transmission delay at junction on reentry tion at PMJs. We counted the number of successful and failed dynamics is not straightforward to assess. While reduction of the propagations at PMJs for both bidirectional conductions during transmission delay causes safer conduction and provides a pathway reentry. The ratio of conduction success for anterograde for reentrant wavefronts, slow conduction through the PMJs can propagation was higher than that for retrograde propagation. be arrhythmogenic as it may assist survival due to increased This can be attributed to the longer refractory period of Purkinje effective path length. cells and almost simultaneous activation of close PMJs due to rapid The average ventricular MFR was unaffected by Purkinje conduction in the Purkinje system. system parameters and similar to the dominant frequency (DF) of For a higher PMJ density, the activation wavefront has a higher ECG reported in experimental studies (average . 8 Hz) for VF in chance of finding a pathway through the Purkinje system which healthy rabbit heart [31], and higher than similar modeling study increases the ratio of bidirectional conduction success and is without Purkinje system (average & 6 Hz) [32]. This is in favorable to maintenance of reentry. The results summarized in agreement with reported simulation results for ventricular model Fig. 5 suggest that number of phase singularities change with and without Purkinje system [18]. This suggests that the proportionally with PMJ density. We attribute these changes to Purkinje system serves to reduce the reentry pathlength to the

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Figure 7. Effects of PMJ size on reentr. A) Sensitivity of average MFR in Purkinje system to the size of PMJ B) Sensitivity of WBI on epicardium to size of PMJ (RPMJ =20MV). doi:10.1371/journal.pone.0088000.g007 minimum one, which depends on the ventricular refractory Although in this study we set junctional parameters so that period. The overall complexity of reentry was mostly governed transmission delay across PMJs are within physiological range by cardiac wavelength and ventricular size and geometry, and [16,17], arrhythmogenic effects of drugs which manipulate does not appear to be significantly affected by Purkinje system junctional coupling at PMJs can be investigated using the same complexity. modeling scheme. An example is octanol which increases gap junctional resistance. In a study on canine subendocardial Purkinje Implications for Pathophysiology and Aging to ventricular transmission, it was revealed that octanol causes a Experimentally it was found that aging is associated with selective delay across PMJs which is believed to be mainly result of functional and topological changes in Purkinje system [5]. These increase in junctional resistance [34]. Other diseases that affect include thinning of Purkinje fibers and a decreased number of cellular coupling, such as through changes in gap junction connections. This in itself is probably antiarrhythmic since it will expression or fibrosis, will also affect the number of functional reduce the probability of a afterdepolarization arising in the PMJs [4]. Purkinje system, without compromising activation or increasing complexity of any arrhythmias which arise. However, to Study Limitations investigate aging effects on ventricular arrhythmia, other age- A shortcoming of our model is the simplification in modeling of related changes such as increase in ventricular stiffness and wall PMJs structure and distribution which is a result of limited thickness, and electrical remodeling must be considered. quantitative data available on the morphology and functioning of Another application of our study is assessing Purkinje system the junctions. The model does not explicitly incorporate transi- contribution to arrhythmias in pathological conditions that lead to tional cells which couple Purkinje cells to ventricular myocytes ventricular remodeling such as (DCM) [15,35]. Nonetheless, due to the design of the model with its and hypertrophic cardiomyopathy (HCM). Previously DCM and asymmetrical loading and source effects, it reproduces retrograde HCM have been modeled by increased wall thickness and and anterograde transmission features, recreates measured junc- increased ventricular diameter, respectively [7]. Assuming that tional action potential traces, and effectively excites the ventricles. Purkinje system branches and PMJs are not affected in ventricular Also PMJs were distributed uniformly on the branches of Purkinje remodeling, it was suggested that HCM has a higher than usual system while the location of PMJs on the subendocardial layer has PMJ density due to a smaller endocardial surface while the DCM not been identified. has a lower density due to larger endocardial surface. By varying In addition, validation of the model parameters and results the number of PMJs, we also implemented these changes in PMJ based on results from experimental studies on rabbit heart may not density, but also studied the consequences on reentry dynamics. be always practicable due to lack of experimental data, for For example, clinical reports indicate that occurrence of lethal instance, recording of Purkinje system electrical activity during ventricular tachyarrhythmias in patients with HCM reduces with arrhythmia has practical limitations which restricts us to quantify age, and in old patients, mortality is unassociated with HCM [33]. the accuracy of the model. Also VF mostly occurs in diseased A possible factor is the reduction of the number of connections hearts, whereas we simulated VF in healthy rabbit heart and VF between the Purkinje system and myocardial tissue with age, mechanisms may be affected by abnormalities in cardiac tissue. which will make reentry simpler.

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One issue not addressed is the increased propensity for Author Contributions afterdepolarizations with an increased Purkinje system. With Conceived and designed the experiments: EB AN EJV. Performed the more PMJs and more arborizations, there would be more Purkinje experiments: EB. Analyzed the data: EB AN EJV. Contributed reagents/ cells susceptible to afterdepolarization generation. The increase in materials/analysis tools: EJV. Wrote the paper: EB EJV. afterdepolarization probability would be proportional to the length of the Purkinje system.

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PLOS ONE | www.plosone.org 9 February 2014 | Volume 9 | Issue 2 | e88000